Design and Analysis, Fourth Edition, by Keppel and Wickens Chapter 4: Analytical Comparisons Among Means | SAS Textbook Examples

Data from Chapter 2 from Table 2.2, page 22

data table2_2;
input a score;
datalines;
1 16 
1 18
1 10 
1 12
1 19
2 4
2 7
2 8
2 10
2 1
3 2
3 10
3 9
3 13 
3 11
;
run;

Table 4.4, page 70. Orthogonal contrasts in a one-way analysis of variance
NOTE1: Contrasts in SAS are performed through the contrast statement.
NOTE2: The orthogonal contrast exclusively partitions the model sums of squares between the two comparisons (i.e., the sum of the contrast sums of squares equals the sum of squares for the model).

proc glm data = table2_2;
class a;
model score = a/ ss3;
contrast 'comp1' a 0 1 -1;
contrast 'comp2' a 1 -.5 -.5; 
run; quit;

The GLM Procedure

   Class Level Information
Class         Levels    Values
a                  3    1 2 3

Number of observations    15

Dependent Variable: score
                                        Sum of
Source                      DF         Squares     Mean Square    F Value    Pr > F
Model                        2     210.0000000     105.0000000       7.00    0.0097
Error                       12     180.0000000      15.0000000
Corrected Total             14     390.0000000

R-Square     Coeff Var      Root MSE    score Mean
0.538462      38.72983      3.872983      10.00000

Source                      DF     Type III SS     Mean Square    F Value    Pr > F
a                            2     210.0000000     105.0000000       7.00    0.0097

Contrast                    DF     Contrast SS     Mean Square    F Value    Pr > F
comp1                        1      22.5000000      22.5000000       1.50    0.2442
comp2                        1     187.5000000     187.5000000      12.50    0.0041

Non-orthogonal contrast in a one-way analysis of variance, top of page 78
NOTE: Unlike the previous orthogonal contrast, a non-orthogonal contrast does not uniquely partition the model sum of squares.

proc glm data = table2_2;
class a;
model score = a/ ss3;
contrast 'comp1' a 1 -1 0;
contrast 'comp2' a 1 0 -1; 
run; quit;

The GLM Procedure

   Class Level Information
Class         Levels    Values
a                  3    1 2 3

Number of observations    15

Dependent Variable: score
                                        Sum of
Source                      DF         Squares     Mean Square    F Value    Pr > F
Model                        2     210.0000000     105.0000000       7.00    0.0097
Error                       12     180.0000000      15.0000000
Corrected Total             14     390.0000000

R-Square     Coeff Var      Root MSE    score Mean
0.538462      38.72983      3.872983      10.00000

Source                      DF     Type III SS     Mean Square    F Value    Pr > F
a                            2     210.0000000     105.0000000       7.00    0.0097

Contrast                    DF     Contrast SS     Mean Square    F Value    Pr > F
comp1                        1     202.5000000     202.5000000      13.50    0.0032
comp2                        1      90.0000000      90.0000000       6.00    0.0306